Preliminaries

Load packages

8.1 μs

Plots.PGFPlotsXBackend

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begin
    using Empirikos
    using DataFrames
    using MosekTools
    using LaTeXStrings
    using Plots
    pgfplotsx()
end

30.6 s

Load the Moving to Opportunities neighborhoods dataset (Chetty and Hendren, 2018) and remove missing entries

3.6 μs

nbhood_csv

	CZ	Name_of_CZ	Census_2000_population	State_Abbrev.	State	Urban_Areas	p25_coef	p25_se	p25_se_boot
	Int64	String	Float64	String	String	Int64	Float64	Float64	Float64
1	100	"Johnson City"	576081.0	"TN"	"Tennessee"	1	-0.416	0.25	0.273
2	200	"Morristown"	227816.0	"TN"	"Tennessee"	1	-0.043	0.249	0.266
3	301	"Middlesborough"	66708.0	"TN"	"Tennessee"	0	0.428	0.568	0.578
4	302	"Knoxville"	727600.0	"TN"	"Tennessee"	1	-0.055	0.183	0.187
5	401	"Winston-Salem"	493180.0	"NC"	"North Carolina"	1	-0.443	0.199	0.201
6	402	"Martinsville"	92753.0	"VA"	"Virginia"	0	-0.47	0.413	0.411
7	500	"Greensboro"	1.05513e6	"NC"	"North Carolina"	1	-0.347	0.132	0.134
8	601	"North Wilkesboro"	90016.0	"NC"	"North Carolina"	0	0.237	0.572	0.519
9	602	"Galax"	64676.0	"VA"	"Virginia"	0	-1.085	0.692	0.806
10	700	"Spartanburg"	354533.0	"SC"	"South Carolina"	1	-0.233	0.23	0.243
more
595	39400	"Seattle"	3.77574e6	"WA"	"Washington"	1	0.229	0.082	0.089

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nbhood_csv = Empirikos.Neighborhoods.load_table() |> DataFrame |> dropmissing

14.0 s

Wrap the data in a type that represents the Gaussian likelihood:

2.9 μs

Empirikos.NormalSample{Float64,Float64}1

Z=  -0.416 | σ=0.25

Z=  -0.043 | σ=0.249

Z=   0.428 | σ=0.568

Z=  -0.055 | σ=0.183

Z=  -0.443 | σ=0.199

Z=   -0.47 | σ=0.413

Z=  -0.347 | σ=0.132

Z=   0.237 | σ=0.572

Z=  -1.085 | σ=0.692

Z=  -0.233 | σ=0.23

Z=  -0.402 | σ=0.2

Z=  -0.248 | σ=0.096

Z=    0.86 | σ=0.601

Z=  -0.386 | σ=0.353

Z=  -0.007 | σ=0.222

Z=  -0.693 | σ=0.763

Z=   0.692 | σ=0.848

Z=  -0.425 | σ=0.239

Z=  -0.172 | σ=0.759

Z=   0.052 | σ=0.358

more586

Z=   0.141 | σ=0.51

587

Z=  -0.053 | σ=0.135

588

Z=  -0.258 | σ=0.348

589

Z=   0.243 | σ=0.248

590

Z=  -0.171 | σ=0.212

591

Z=   0.807 | σ=0.59

592

Z=    0.19 | σ=0.258

593

Z=   0.331 | σ=0.355

594

Z=   0.723 | σ=0.424

595

Z=   0.229 | σ=0.082

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Zs = NormalSample.(nbhood_csv.p25_coef, nbhood_csv.p25_se)

63.1 ms

Let us define the empirical Bayes targets we want to estimate. We will estimate $E [μ ∣ Z = z, σ = σ]$ where we vary $σ \in {0.5, 1, 2}$ and $z \in {- 3 σ, - 2.9 σ, \dots, 2.9 σ, 3 σ}$ .

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md" Let us define the empirical Bayes targets we want to estimate. We will estimate $\mathbb E[\mu \mid Z=z, σ = σ]$ where we vary $\sigma \in \{0.5, 1, 2\}$ and $z \in \{-3\sigma, -2.9\sigma,\dotsc, 2.9\sigma, 3\sigma\}$."

3.6 μs

σs

1×3 Array{Float64,2}:
 0.5  1.0  2.0

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σs = [0.5 1.0 2.0]

635 ns

targets

61×3 Array{PosteriorMean{NormalSample{Float64,Float64}},2}:
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.5 | σ=0.5  )  …  PosteriorMean{NormalSample{Float64,Float64}}(Z=    -6.0 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.45 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.8 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.4 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.6 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.35 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.4 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.3 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.2 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.25 | σ=0.5  )  …  PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.0 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.2 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=    -4.8 | σ=2.0  )
 ⋮                                                                   ⋱  
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.25 | σ=0.5  )  …  PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.0 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.3 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.2 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.35 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.4 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.4 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.6 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.45 | σ=0.5  )     PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.8 | σ=2.0  )
 PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.5 | σ=0.5  )  …  PosteriorMean{NormalSample{Float64,Float64}}(Z=     6.0 | σ=2.0  )

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targets = PosteriorMean.(NormalSample.(collect(-3:0.1:3) .* σs, σs))

116 ms

target_names

1×3 Array{LaTeXString,2}:
 L"$E[\mu \mid Z=z, \sigma=0.5]$"  …  L"$E[\mu \mid Z=z, \sigma=2.0]$"

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target_names = [L"E[\mu \mid Z=z, \sigma=%$σ]" for σ in σs]

48.1 ms

Smooth prior class

Throughout this Section we first assume that the true prior $G$ is smooth and lies in the class of mixtures of

${N (μ, {0.25}^{2}), μ \in {- 3, - 2.9, \dots, 3}} .$

4.1 μs

gcal_smooth

MixturePriorClass (K = 601)
Distributions.Normal{Float64}(μ=-3.0, σ=0.25)
Distributions.Normal{Float64}(μ=-2.99, σ=0.25)
Distributions.Normal{Float64}(μ=-2.98, σ=0.25)
Distributions.Normal{Float64}(μ=-2.97, σ=0.25)
Distributions.Normal{Float64}(μ=-2.96, σ=0.25)
Distributions.Normal{Float64}(μ=-2.95, σ=0.25)
Distributions.Normal{Float64}(μ=-2.94, σ=0.25)
Distributions.Normal{Float64}(μ=-2.93, σ=0.25)
The rest are omitted ...

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gcal_smooth = MixturePriorClass(Normal.(-3:0.01:3, 0.25))

74.9 ms

We start by fitting the NPMLE to that prior class (this is not needed for the intervals).

2.9 μs

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npmle_smooth_fit = fit(NPMLE(gcal_smooth, Mosek.Optimizer), Zs);

18.3 s

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plot(
    -3:0.001:3,
    x -> pdf(npmle_smooth_fit.prior, x),
    xguide = L"\mu",
    yguide = L"g(\mu)",
    title = "NPMLE prior estimate",
    label = nothing,
    size = (400,200)
)

8.4 s

Start with confidence interval construction (compound DKW-F-Localization)

3.0 μs

floc_method_smooth

FLocalizationInterval{DvoretzkyKieferWolfowitz{Float64,Int64},MixturePriorClass{Array{Normal{Float64},1}}}flocalizationDvoretzkyKieferWolfowitz{Float64,Int64}α

0.05

max_constraints

convexclass

MixturePriorClass (K = 601)
Distributions.Normal{Float64}(μ=-3.0, σ=0.25)
Distributions.Normal{Float64}(μ=-2.99, σ=0.25)
Distributions.Normal{Float64}(μ=-2.98, σ=0.25)
Distributions.Normal{Float64}(μ=-2.97, σ=0.25)
Distributions.Normal{Float64}(μ=-2.96, σ=0.25)
Distributions.Normal{Float64}(μ=-2.95, σ=0.25)
Distributions.Normal{Float64}(μ=-2.94, σ=0.25)
Distributions.Normal{Float64}(μ=-2.93, σ=0.25)
The rest are omitted ...

solver

Optimizer (generic function with 2 methods)

n_bisection

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floc_method_smooth = FLocalizationInterval(;
    flocalization = DvoretzkyKieferWolfowitz(0.05),
    convexclass = gcal_smooth,
    solver = Mosek.Optimizer,
)

24.4 ms

postmean_cis_smooth

61×3 Array{Empirikos.LowerUpperConfidenceInterval,2}:
 lower = -1.244, upper = -0.2099, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.5 | σ=0.5  ))   …  lower = -1.587, upper = 0.01869, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -6.0 | σ=2.0  ))
 lower = -1.113, upper = -0.1999, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.45 | σ=0.5  ))      lower = -1.465, upper = 0.02154, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.8 | σ=2.0  ))
 lower = -0.9878, upper = -0.1899, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.4 | σ=0.5  ))     lower = -1.344, upper = 0.02484, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.6 | σ=2.0  ))
 lower = -0.8702, upper = -0.1799, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.35 | σ=0.5  ))     lower = -1.224, upper = 0.02792, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.4 | σ=2.0  ))
 lower = -0.7615, upper = -0.1699, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.3 | σ=0.5  ))     lower = -1.108, upper = 0.031, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.2 | σ=2.0  ))
 lower = -0.6629, upper = -0.1591, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.25 | σ=0.5  ))  …  lower = -0.9958, upper = 0.03407, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.0 | σ=2.0  ))
 lower = -0.5747, upper = -0.144, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.2 | σ=0.5  ))      lower = -0.889, upper = 0.03715, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -4.8 | σ=2.0  ))
 ⋮                                                                                                                 ⋱  
 lower = 0.304, upper = 0.9541, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.25 | σ=0.5  ))     …  lower = 0.1529, upper = 1.584, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.0 | σ=2.0  ))
 lower = 0.3213, upper = 1.049, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.3 | σ=0.5  ))        lower = 0.156, upper = 1.691, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.2 | σ=2.0  ))
 lower = 0.3318, upper = 1.142, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.35 | σ=0.5  ))        lower = 0.1591, upper = 1.797, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.4 | σ=2.0  ))
 lower = 0.3418, upper = 1.24, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.4 | σ=0.5  ))         lower = 0.1621, upper = 1.902, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.6 | σ=2.0  ))
 lower = 0.3518, upper = 1.337, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.45 | σ=0.5  ))        lower = 0.1654, upper = 2.004, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.8 | σ=2.0  ))
 lower = 0.3618, upper = 1.429, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.5 | σ=0.5  ))     …  lower = 0.1683, upper = 2.102, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     6.0 | σ=2.0  ))

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postmean_cis_smooth = confint.(floc_method_smooth, targets,Zs)
​

130 s

Also evaluate the plugin estimates based on the NPMLE and finally plot everything (interval bands in blue, NPMLE estimate in dashed purple and z ↦ z dotted black).

6.9 μs

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targets_smooth_npmle = targets.(npmle_smooth_fit.prior);

87.7 ms

x
 
begin
plots_smooth = plot.(Ref(-3:0.1:3),eachcol(postmean_cis_smooth), xlabel = L"z / \sigma", label = "")
plot!.(
    plots_smooth,
    Ref(-3:0.1:3.0),
    eachcol(response.(location.(targets))),
    label = "",
    seriestype = :line,
    linestyle = :dot,
    seriescolor = :gray,
)
plot!.(
    plots_smooth,
    Ref(-3:0.1:3.0),
    eachcol(targets_smooth_npmle),
    label = "",
    seriestype = :line,
    linecolor = :purple,
    linestyle = :dash,
)
plot(plots_smooth..., ylabel = target_names, layout=(1,3), size=(600,200))
end

113 ms

Discrete class

Now instead we make a more standard nonparametric EB assumption, i.e. that $G$ is an arbitrary discrete distribution supported on the grid $- 3, - 2.9, \dots, 2.9, 3$ and repeat the same steps as we did for the smooth class above.

5.2 μs

discrete_class

DiscretePriorClass | support = -3.0:0.01:3.0

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discrete_class = Empirikos.DiscretePriorClass(-3:0.01:3)

4.3 ms

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npmle_discrete_fit = fit(NPMLE(discrete_class, Mosek.Optimizer), Zs);

1.7 s

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plot(
    support(npmle_discrete_fit.prior),
    probs(npmle_discrete_fit.prior),
    seriestype = :sticks,
    xguide = L"\mu",
    yguide = L"g(\mu)",
    title = "NPMLE prior estimate",
    label = nothing,
    size = (400,200)
)

127 ms

floc_method_discrete

FLocalizationInterval{DvoretzkyKieferWolfowitz{Float64,Int64},DiscretePriorClass{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}}flocalizationDvoretzkyKieferWolfowitz{Float64,Int64}α

0.05

max_constraints

convexclass

DiscretePriorClass | support = -3.0:0.01:3.0

solver

Optimizer (generic function with 2 methods)

n_bisection

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floc_method_discrete = FLocalizationInterval(;
    flocalization = DvoretzkyKieferWolfowitz(0.05),
    convexclass = discrete_class,
    solver = Mosek.Optimizer,
)

13.3 ms

39.0 ns

postmean_cis_discrete

61×3 Array{Empirikos.LowerUpperConfidenceInterval,2}:
 lower = -1.709, upper = 0.09511, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.5 | σ=0.5  ))  …  lower = -1.96, upper = 0.09678, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -6.0 | σ=2.0  ))
 lower = -1.562, upper = 0.09512, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.45 | σ=0.5  ))     lower = -1.851, upper = 0.09713, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.8 | σ=2.0  ))
 lower = -1.413, upper = 0.09512, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.4 | σ=0.5  ))     lower = -1.737, upper = 0.09728, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.6 | σ=2.0  ))
 lower = -1.265, upper = 0.09513, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.35 | σ=0.5  ))     lower = -1.62, upper = 0.09766, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.4 | σ=2.0  ))
 lower = -1.119, upper = 0.09513, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.3 | σ=0.5  ))     lower = -1.5, upper = 0.09824, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.2 | σ=2.0  ))
 lower = -0.977, upper = 0.1022, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=   -1.25 | σ=0.5  ))   …  lower = -1.38, upper = 0.09901, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -5.0 | σ=2.0  ))
 lower = -0.8433, upper = 0.1089, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -1.2 | σ=0.5  ))     lower = -1.26, upper = 0.1, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    -4.8 | σ=2.0  ))
 ⋮                                                                                                                ⋱  
 lower = 0.01533, upper = 1.175, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.25 | σ=0.5  ))   …  lower = 0.08832, upper = 1.598, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.0 | σ=2.0  ))
 lower = 0.02487, upper = 1.283, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.3 | σ=0.5  ))      lower = 0.09044, upper = 1.708, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.2 | σ=2.0  ))
 lower = 0.04172, upper = 1.382, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.35 | σ=0.5  ))      lower = 0.09243, upper = 1.816, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.4 | σ=2.0  ))
 lower = 0.06855, upper = 1.496, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.4 | σ=0.5  ))      lower = 0.09438, upper = 1.921, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.6 | σ=2.0  ))
 lower = 0.09328, upper = 1.619, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=    1.45 | σ=0.5  ))      lower = 0.09638, upper = 2.022, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     5.8 | σ=2.0  ))
 lower = 0.1057, upper = 1.731, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     1.5 | σ=0.5  ))    …  lower = 0.09841, upper = 2.117, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=     6.0 | σ=2.0  ))

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postmean_cis_discrete = confint.(floc_method_discrete, targets, Zs)

137 s

targets_discrete_npmle

61×3 Array{Float64,2}:
 -0.0661083  -0.0313622  -0.00599918
 -0.0639283  -0.0300027  -0.00496677
 -0.0617293  -0.0286258  -0.00391495
 -0.0595121  -0.02723    -0.00284286
 -0.0572774  -0.025814   -0.00174962
 -0.0550258  -0.0243759  -0.000634291
 -0.0527579  -0.022914    0.000504118
  ⋮                      
  0.410241    0.254003    0.139249
  0.448052    0.27757     0.147126
  0.486403    0.304242    0.155606
  0.524787    0.334624    0.164754
  0.562703    0.369437    0.174644
  0.599696    0.409529    0.185357

x
 
targets_discrete_npmle = targets.(npmle_discrete_fit.prior)

2.5 ms

x
 
begin
plots_discrete = plot.(Ref(-3:0.1:3), 
    eachcol(postmean_cis_discrete), 
    xlabel = L"z/\sigma", 
    label = ""
)
plot!.(
    plots_discrete,
    Ref(-3:0.1:3.0),
    eachcol(response.(location.(targets))),
    label = "",
    seriestype = :line,
    linestyle = :dot,
    seriescolor = :gray,
)
plot!.(
    plots_discrete,
    Ref(-3:0.1:3.0),
    eachcol(targets_discrete_npmle),
    label = "",
    seriestype = :line,
    linecolor = :purple,
    linestyle = :dash,
)
plot(plots_discrete..., ylabel = target_names, layout=(1,3), size=(600,200))
end

10.4 ms

1×3 Array{Array{Float64,1},2}:
 [-1.5, 1.5]  [-3.0, 3.0]  [-6.0, 6.0]

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[[-3σ;3σ] for σ ∈ σs]

2.4 μs

AMARI intervals

Here we also show how the AMARI intervals may be computed. We assume that the prior lies in the discrete prior class and also compare AMARI intervals to the compound-F-localization intervals (for the posterior mean of the neighborhood causal effect of Yuma).

7.7 μs

yuma_df

	CZ	Name_of_CZ	Census_2000_population	State_Abbrev.	State	Urban_Areas	p25_coef	p25_se	p25_se_boot
	Int64	String	Float64	String	String	Int64	Float64	Float64	Float64
1	38100	"Yuma"	302387.0	"CA"	"California"	1	-0.216	0.172	0.175

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yuma_df = filter(:Name_of_CZ => isequal("Yuma"), nbhood_csv)

199 ms

yuma_posterior_mean

PosteriorMean{NormalSample{Float64,Float64}}Z

Z=  -0.216 | σ=0.172

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yuma_posterior_mean = PosteriorMean(NormalSample(yuma_df.p25_coef[1], 
                                                 yuma_df.p25_se[1]))

6.3 ms

Let us first look at the plug-in estimate from the NPMLE.

2.9 μs

-0.0641787365657269

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yuma_posterior_mean(npmle_discrete_fit.prior)

18.1 μs

Next we compute the compound-F-localization interval:

2.8 μs

ci_floc

lower = -0.2179, upper = 0.1232, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=  -0.216 | σ=0.172))

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ci_floc = confint(floc_method_discrete, yuma_posterior_mean, Zs)

23.1 s

And finally the AMARI interval.

2.7 μs

amari

AMARI{DvoretzkyKieferWolfowitz{Float64,Int64},DiscretePriorClass{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}},DataType,Nothing}convexclass

DiscretePriorClass | support = -3.0:0.01:3.0

flocalizationDvoretzkyKieferWolfowitz{Float64,Int64}α

0.01

max_constraints

solver

Optimizer (generic function with 2 methods)

discretizer

nothing

plugin_GEmpirikos.FittedConvexMinimumDistance{DiscreteNonParametric{Float64,Float64,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}},Array{Float64,1}},NPMLE{DiscretePriorClass{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}}}prior

Distributions.DiscreteNonParametric{Float64,Float64,StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}},Array{Float64,1}}(
support: -3.0:0.01:3.0
p: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  1.3720672434787157e-6, 6.081756595587953e-7, 2.983556408753117e-7, 1.7533507114523433e-7, 1.1932343416975139e-7, 8.976114118617694e-8, 7.192214655252968e-8, 5.984916643357872e-8, 5.0918732423268294e-8, 4.3894711195395335e-8]
)

methodNPMLE{DiscretePriorClass{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}}convexclass

DiscretePriorClass | support = -3.0:0.01:3.0

solver

Optimizer (generic function with 2 methods)

dictPairsmodel

$\text{$$ \begin{alignat*}{1}\min\quad & u\\ \text{Subject to} \quad & noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + noname + 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] \in MathOptInterface.RelativeEntropyCone(1191)\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ & noname \geq 0.0\\ \end{alignat*} $$}$

data_split

:none

delta_grid

0.2:0.5:6.7

delta_objectiveEmpirikos.RMSE{DataBasedDefault}nDataBasedDefaultmodulus_model

Empirikos.ModulusModelWithoutF

representative_eb_samples

nothing

nothing

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amari = AMARI(; convexclass = discrete_class,
                flocalization = DvoretzkyKieferWolfowitz(0.01),
                plugin_G = npmle_discrete_fit,
                solver=Mosek.Optimizer)

37.2 ms

ci_amari

lower = -0.1011, upper = -0.02174, α = 0.05  (PosteriorMean{NormalSample{Float64,Float64}}(Z=  -0.216 | σ=0.172))

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ci_amari = confint(amari, yuma_posterior_mean, Zs)

686 s

The AMARI interval does not contain zero (and so we can reject the null that the posterior mean for Yuma is nonnegative), while the F-localization intervals do contain zero.

3.4 μs